Problem with finding the Equation of a Surface

[Edder]

Hey everyone,

I am having some problems in solving a problem regarding surface equation. It says: A line passes through the points P(0,-1,0) and Q(-1,-1,1), find the equation of the surface generated by this line when it rotates around the z-axis. (Such a surface is called a ruled surface)

How would I go about solving this? I am not quite sure what method to use here.

Any help and feedback appreciated, thanks.

 

[HallsofIvy]

Step one would be to find parametric equations for the line. Then use the fact that a point (x, y, z), rotated around the z-axis will have coordinates \(\displaystyle (\sqrt{x^2+ y^2}cos(\theta), \sqrt{x^2+ y^2}sin(\theta), z)\) for \(\displaystyle 0\le \theta< 2\pi\).

 

[Edder]

Step one would be to find parametric equations for the line. Then use the fact that a point (x, y, z), rotated around the z-axis will have coordnates \(\displaystyle (\sqrt{x^2+ y^2}cos(\theta), \sqrt{x^2+ y^2}sin(\theta), z)\) for \(\displaystyle 0\le \theta< 2\pi\).

Thanks man, appreciate it.